In this work, both positive and negative corona discharge of pin-grid geometrical configuration was studied and the necessary modification of the general law of corona discharge was proposed. The current-voltage measurements were performed at room temperature and at different inter electrode separations. The variation of dimensional constant K and corona inception voltage Vo with pin-grid separations S were subjected into the general law of corona discharge using the least square fitting method in Log-Log scale. The relationship between corona current and different voltage (V-Vo) was investigated to find the acceptable value of exponent n. The least square fitting for all variations of corona parameters was based on the highest R-square value of obtained straight lines for individual measurements. It was found that value of exponent n for both polarities is larger compared to the empirical formula proposed previously for the general law of corona discharge.